Analysis of 1D Magneto-Electro-Elastic Smart Beam using 2D Finite Elements

Multiphase Magneto-Electro-Elastic (MEE) 1D beams of BaTiO_3-CoFe₂O₄smart composite are modeled. The Six multiphase beams are obtained by varying <i>V</i>_<em>f</em> of BaTiO₃ in BaTiO_3-CoFe₂O₄, in steps of 20%, from 0% to 100%, to capture the electric, magnetic, and elastic behavior effectively. The 2D FE model for the smart beam is developed using constitutive equations of 3D MEE solid. The FE model uses 2D iso-parametric finite elements with four <i>dof</i>/<i>node</i> to compute the transverse displacement, electric &amp; magnetic potential, induced stresses, and electric &amp; magnetic variables. The developed 2D FE model is validated and effectively calculates the magnetoelectric effect in the multiphase smart 1D beams. The study is extended for two end conditions of MEE beam, (viz., simply supported and cantilever) and two types of mechanical loads. (viz., UDL and point loads).

针对钛酸钡-钴铁氧体（BaTiO₃-CoFe₂O₄）智能复合材料的多相磁电弹性（Magneto-Electro-Elastic, MEE）一维梁开展建模研究。为有效捕捉其电、磁与弹性力学行为，通过以20%为步长，在0%至100%范围内调整钛酸钡在钛酸钡-钴铁氧体中的体积分数（Volume fraction, V_f），得到六组多相梁。基于三维磁电弹性固体的本构方程，构建该智能梁的二维有限元（Finite Element, FE）模型；该模型采用每节点包含4个自由度（Degree of Freedom, dof）的二维等参有限元，可计算横向位移、电磁势、诱导应力以及电磁变量。所构建的二维有限元模型经过验证，可有效计算多相智能一维梁的磁电效应。本研究进一步拓展至磁电弹性梁的两类边界条件（即简支与悬臂）以及两类机械载荷场景（即均布载荷（Uniform Distributed Load, UDL）与集中载荷）的分析。